As you can see 8-bit/color RGBA is actually what Paint.NET calls a 32-bit PNG, because it's 8 bits per color * (3 colors + 1 alpha channel). 8 * 4 = 32. A 24-bit PNG is the same, but without the alpha channel: 8 * 3 = 24.

If you want what Paint.NET calls a 24-bit PNG, you need to remove the alpha channel. As far as I can tell, GIMP always exports a PNG with an alpha channel if any of your layers has an alpha channel.

If you're only using 1 layer, then it's simple: Go to Layer > Transparency > Remove Alpha Channel and then export. You'll get a 24-bit PNG.

If you're using multiple layers and need transparency effects, then jthill pointed out that you can use Image > Flatten Image to remove the layers with transparency before exporting. You can then Undo to restore the layers.

You can also post-process the exported PNG to remove the alpha channel. You could load the exported image back into GIMP, which will make it 1 layer, remove the alpha channel from that layer, and export again. A better way is to use optipng, which will usually compress a PNG better than GIMP can in addition to removing a useless alpha channel.

NOTE: If you're looking for 16-bits per channel support then this answer applies to that. Otherwise if you're miss understanding 24-bit support (8-bit * 3 colors (RGB) = 24-bits, then see @cjm's answer as to how to understand how that works.

For some industries, especially photography, 24-bit colour depths (8 bits per channel) are a real barrier to entry. Once again, it's GEGL to the rescue. Work on integrating GEGL into GIMP began after 2.4 was released, and will span across several stable releases. This work will be completed in GIMP 3.0, which will have full support for high bit depths. If you need such support now and can't wait, cinepaint and Krita support 16 bits per channel now.

The current development branch, GIMP 2.9.x, supports higher bit depths than the 2.8 and older 8-Bit-per-component...

GEGL provides infrastructure to do demand based cached non destructive image editing on larger than RAM buffers. Through babl it provides support for a wide range of color models and pixel storage formats for input and output.

Features

Floating point handling and processing and output of larger 8bit, 16bit integer and 32bit floating